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1. Write the given English phrase as an expression or equation: a. the sum of five and three times a number ans: 5 + 3x or 3x + 5 b. the product of three and a number, decreased by ten, is 25 ans: 3x − 10 = 25 c. The difference of a number and twelve. ans: x − 12 d. Fourteen subtracted by a number times three. ans: 3x − 14 e. The product of ten and Four less than a number. ans: 10(x − 4) f. The quotient of a number and 5. x ans: 5 g. When a number is decreased by four, the result is twenty. ans: x − 4 = 20 h. The sum of ten and three times a number is five more than twice the number. ans: 10 + 3x = 5 + 2x i. The quotient of a number and seven, increased by five, is three less than twice the number. x ans: + 5 = 2x − 3 7 2. Consider the following numbers: √ 2 0 2 √ 10 2 {−10, −8, −5, − , 0, 1, 2, , , , π, 16, } 3 3 3 0 5 a. List all the natural numbers √ 10 =2 ans: 1, 16 = 4, 5 b. List all the integers √ 10 0 ans: 1, 16 = 4, = 2, −10, −8, −5, 0, = 0 5 3 c. List all the rational numbers √ 10 0 2 2 ans: 1, 16 = 4, = 2, −10, −8, −5, 0, = 0, − , 5 3 3 3 d. List all the irrational numbers √ ans: 2, π e. List all the real numbers √ 10 0 2 2 √ ans: 1, 16 = 4, = 2, −10, −8, −5, 0, = 0, − , , 2, π 5 3 3 3 3. Consider the following numbers: 1 1 √ 2 101 , 2, , π, , 4 1 21 a. List all the natural numbers 2 ans: = 2 1 b. List all the integers −5, −1, 0, 5 0 2 = 2, −5, −1, 0 1 c. List all the rational numbers 1 101 2 ans: = 2, −5, −1, 0, , 1 4 21 d. List all the irrational numbers √ ans: 2, π ans: e. List all the real numbers 2 1 101 √ ans: = 2, −5, −1, 0, , , 2, π 1 4 21 4. Consider the given numbers: √ 1 2 8 , 1, , 4, −3, − , 2, 4 3 3 a. List all the natural numbers. π, √ −2 ans: 1, 4 b. List all the integers. 8 = −2 4 c. List all the rational numbers. 8 1 2 ans: 1, 4, −3, − , , 4 3 3 d. List all the irrational numbers. √ ans: 2, π ans: 1, 4, −3, − e. List all the real numbers. 8 1 2 √ ans: 1, 4, −3, − , , , 2, π 4 3 3 2 5. Which of the following are natural number: I −2 II 3 III 25 a. I only b. I and II only them are natural numbers c. II and III only d. they are all natural numbers e. None of ans: c 6. Which of the following are integer: I −5 4 II 2 III 0 a. I only integer b. I and III only c. III only d. They are all integers e. None of them is an ans: d 7. Which of the following are rational number: −3 1 II 4 III π I a. I only b. I and II only a rational number c. II only d. They are all rational numbers e. None of them is ans: b 8. Which of the following are real number: 0 4 5 II 0 π III 2 a. I only b. I and II only is a real number I c. I and III only d. They are all real numbers ans: c 3 e. None of them 9. Which of the following statement(s) is/are true? I A real number is always a rational number. II An integer is never a natural number. III An irrational number is always a real number. a. I only b. II only c. III only d. They are all true e. They are all false ans: c 10. Which of the following statement(s) is/are true? I An irrational number is never a rational number. II A real number is always an integer. III A natural number is always a rational number. a. I only b. II only c. III only d. I and III only ans: d 11. True of False: a. A natural number is never an integer. ans: False b. A natural number is never negative. ans: True c. An integer is a always rational number. ans: True d. A rational number is never irrational. ans: True e. A real number is never irrational. ans: False f. An irrational number is never an integer. ans: True g. A rational number is sometimes an integer. ans: True 4 e. II and III only 12. Perform the Operation: a. 3 − 5 ans: −2 b. −3 + −5 ans: −8 c. 3 + −5 ans: −2 d. −5 − (−3) ans: −2 e. 14 + −6 ans: 8 f. −12 − (−24) ans: 12 g. 14 + −3 ans: 11 h. −17 − 4 ans: −21 i. −22 + 32 ans: 10 j. −4 · −3 ans: 12 k. 4 · −3 ans: −12 l. −2 · 3 ans: −6 m. −15 ÷ −5 ans: 3 n. 24 ÷ −12 ans: −2 o. −4 ÷ −3 4 ans: 3 p. 12 ÷ −8 ans: − q. 3 2 −3 2 · 4 3 5 ans: − 1 2 5 7 · 21 −4 5 ans: 12 12 −3 ·− s. − 8 5 9 ans: − 10 11 22 t. ·− 18 15 121 ans: − 135 −30 14 u. · 7 3 ans: −20 12 v. ÷3 5 4 ans: 5 21 w. −7 ÷ 4 4 ans: − 3 −30 14 x. ÷ 7 3 45 ans: − 49 24 13 y. − ÷ − 5 23 552 ans: 65 10 21 z. − ÷ 49 6 20 ans: − 343 r. − 6 13. Evaluate the expression: a. 12 − 32 + 2(4 − 2) − 12 ÷ 3 · 2 + 1 ans: 0 b. 4 + 3 · −24 − 2 · 52 − (22 + 6) ans: −104 c. 23 − 4 − 52 − 4 · 2 + 22 6 + −3 ans: 11 d. 3 − (3 + 4 · −6) + −33 − 22 · (5 − 11) ans: 21 e. 4 − 42 + (12 + ans: 22 + −32 · 2) + 21 12 − 32 53 3 f. 2(3 − 12 · 4 −6 + 42 + 1) − 8 · −3 (2 − 4)2 ans: −208 g. (10 + 2) − 10 − (42 − 10) − (−42 − 5) ans: 17 h. 2 + 3 · 4 + (5 − 6) · 72 − 8 ans: −43 14. Evaluate the expression if x = −1, y = 2, and z = −2 a. x2 − 4(y − 2) + z − 3 ans: −4 xy 2 − z + 4x − 2 2x + z − 3 40 ans: − 7 3 c. 3x − 4y + 5z 2 − + 3 − 2y 1−z ans: 7 −x + z d. 2x2 z − yz + 3 − (2y + z) − 2 3 ans: 2 b. e. 10x − 3y − z 3 + 6(x + 3) − 9x ans: 13 15. Which of the following is/are example(s) of the associative property of addition? I 3 + (x + y) = (x + y) + 3 7 II (a + b) + 4 = a + (b + 4) III a(bc) = (ab)c a. I only b. II only c. I and III d. They all are e. None of them is ans: b 16. Which of the following is/are example(s) of the commutative property of multiplication? I 3(x + y) = 3x + 3y II a(x + 4) = (x + 4)a III x(yz) = (xy)z a. I only b. II only c. I and III d. They all are ans: b 8 e. None of them is 17. The equation −2(x + 3) = −2x − 6 is an example of which property of the real numbers? ans: distributive property 18. State the property of the real numbers that justify the statement: x(y + 3) = (y + 3)x ans: commutative property of multiplication 19. State the property of the real numbers that justify the statement: 2a(b − 1) = 2ab − 2a ans: distributive property 20. State the property of the real numbers that justify the statement: x + (y + 2) = (x + y) + 2 ans: associative property of addition 21. Simplify the expression: a. 4x + 5x ans: 9x b. −x − 3(x + 2) ans: −4x − 6 c. 4x − 3x + 3 + 9 − 4(x − 4) ans: −3x + 28 d. 3[x + 4(3x − 7) + 5(2x + 1) − 2] + 4x − 1 ans: 73x − 76 e. 10 − 5(3x − 2) − 4(x + 3) + 9 − 4(2x − 1) ans: −27x + 21 f. x − x + 1 − [x + 2 − (x − 3 − x + 4 − [x − 5 + (x − 6)] + 7x − 8 + 9 − 10x) − 11 + 12x] + 13 ans: −18x + 36 9